Aircraft: B737
Phase of flight: Climb
Anomaly: Aircraft Equipment Problem Less Severe; Deviation / Discrepancy - Procedural Published Material / Policy; Flight Deck / Cabin / Aircraft Event Other / Unknown

Captain (CA)=Pilot Monitoring (PM); First Officer (FO)=Pilot Flying (PF). Discovered pressurization outflow valve in the full open position during the after takeoff checklist (no Auto Fail lights; both Packs; ISO valve and bleeds all in proper position). Discussed with the FO and advised ATC we needed to level off at 10;000 ft to investigate an issue and asked for straight ahead to avoid terrain (initially assigned 15;000 ft on the SID). FO was PF and had them take the radio. Pulled the QRH and referenced AUTO Fail or Unscheduled Pressurization Change 2.2. At this point we discussed and surmised we did NOT have an AUTO Fail issue nor and unscheduled pressurization change as the Cabin appeared to be modestly; although suspiciously pressurizing; as we were building some differential and the cabin altitude was relatively low. Troubleshooting forbids switch manipulation unless inclusive of a QRH or other written procedure hence we chose not to manipulate cabin pressurization controller from AUTO to ATLN. Additionally; we recalled a bulletin from Standards Department dated 7/xx/2020 titled 'Cabin Pressure Controller Blinking/Blanking issue'. This bulletin states that on our 900ER fleet from (tails)(we were in tail) the digital controller can blank and or blink or become so dim its unreadable. Additionally; the bulletin states the controller should right itself shortly...We did not have any blinking/blanking or dimness. Our outflow indicator was bright and solid indicating full open and remained so for the duration of our flight. In an attempt to determine if the cabin would hold we elected to continue our climb to 12;000 ft at which point we got a significant bump felt by the entire crew.... At this point I attempted to contact Dispatch via ACARS to establish two way radio communications. We had plodded along south at a low altitude for a good duration in an attempt to solve the issue. I became concerned with our flight plan fuel. We were dispatched with no reserve for ZZZ1 (weather severe clear at arrival time). Was there enough to complete the mission or might we find ourselves having to divert for fuel 'if' we felt the cabin psi was solid enabling us to continue? We we're now down near (mountain) at 12;000 ft IMC picking up a fair amount of ice as weather was now an issue. After multiple attempts to get a hold of Dispatch to no avail; Flight Attendants complaining about ears; a QRH procedure that didn't quite fit; no ability to troubleshoot; a bulletin that didn't match enough to convince me and a possible fuel stop with an open maintenance issue stranding passengers....in consultation w/ my FO I made the command decision to return to ZZZ. In my mind; this was the safest option and provided our passengers an opportunity to reset. Additionally; it brought the aircraft back to a maintenance base for investigation and repair. We informed Dispatch via ACARS and setup to return and received an amended release via ACARS. We did not declare an emergency as it did not appear warranted/necessary. We ran performance including our LTP (landing threshold point); discussed our TPC and landed significantly under max landing weight as we had a light load. During block in as L1 was opened we felt another pressure bump despite the outflow valve remaining in the full open position. I greeted all deplaning passengers and answered questions; debriefed full crew and discussed scenario and concerns. Flight Attendants met with supervisor and were replaced. No crew members/ nor passengers asked for medical attention. Swapped aircraft; checked duty time and pressed on.Lesson learned:I should have used SATCOM to raise Dispatch in lieu of ACARS. We traveled a fair ways south and company frequency became weak. We switched to XXX.X and sent a message but never could get radio contact. We became distracted by the accumulation of ice buildup at that point in the journey. Bulletin concern: If it is related to the digital controller bulletin why would the company continue to allow problematic controllers be installed? NOTE: The original design Pressurization Control Panel may be installed in any 9ER aircraft from (tail) and subsequent as a repair for a Pressurization Control Panel issue. Therefore; even though (tail) and subs were delivered with the upgraded panel; this issue may occur on these aircraft if the upgraded panel has been replaced with an original panel. Captain reported aircraft failed to pressurize correctly on takeoff and after trouble shooting; elected to do an Air Turn Back.